“…In short, the close similarity of the Si−O bond lengths and Si−O−Si angles and the electron density distributions for a quartz crystal and a gas-phase molecule like H 3 SiOSiH 3 implies that the forces that govern the two structures are short ranged and molecular-like. Also, the bond lengths and angles observed for a relatively large number of silica polymorphs such as quartz have been shown to conform closely with a potential energy surface calculated for the (OH) 3 SiOSi(OH) 3 molecule, again suggesting that the forces that govern the energy of the Si−O bond, Si−O bond lengths, and Si−O−Si angles are molecular-like. 1 Scatter diagrams of the bond critical point (bcp) properties plotted against the experimental bond lengths, R(Si−O) (squares), for a relatively larger number of silicate crystals: 23 (a) R(Si−O) vs ρ( r c ), the value of the electron density, ρ, at the bond critical point, r c ; (b) R(Si−O) vs r b (O), the bonded radius of the O atom; (c) R(Si−O) vs |λ 12 |, where λ 12 = 1/2(λ 1 + λ 2 ) and λ 1 + λ 2 measure the negative curvatures of ρ perpendicular to the bond path at r c ; (d) R(Si−O) vs λ 3 , the positive curvature of ρ measured parallel to the bond path at r c ; and (e) R(Si−O) vs ∇ 2 ρ( r c ), the Laplacian of ρ measured at r c .…”
Section: Si−o Bonded Interactions Of Hydroxyacid Silicate
Molecules A...supporting
confidence: 59%
“…Indeed, Gillespie and Johnson 16 have concluded that the bond comprising the H 3 Si−O−SiH 3 molecule is a highly ionic bond with net atomic charges conferred on Si and O of +3.02 and −1.72 e, respectively. Given the small bending force constant of the Si−O−Si angle, ∼5 N/m, calculated for the (OH) 3 Si−O−Si(OH) 3 molecule, together with a large net atomic charge on Si, it is difficult to reconcile why the angle observed for the molecule is bent at 144°, as observed for cristobalite, rather than straight if the bond is a closed-shell interaction and the charges on the Si atoms are large. Further, it is also notable that Cohen, in a first principles study of crystalline silica, concluded that “SiO 2 is held together by a combination of covalent spσ bonding and ionic bonding between the highly charged tetravalent Si 4+ and O 2- ions”.…”
Section: Si−o Bonded Interactions Of Hydroxyacid Silicate
Molecules A...mentioning
confidence: 99%
“…The electron density along the path at r c is at a minimum value with respect to any displacement parallel to the path but a maximum with respect to any radial displacement perpendicular to the path. The value of ρ( r c ) has been observed to be a direct measure of the strength of a given metal oxygen M−O bond; the greater the value of ρ( r c ), typically the shorter the bond . The trace of the Hessian of ρ( r ), H ij = ∂ 2 ρ( r )/∂x i ∂x j , when evaluated at r c and diagonalized equals the sum of eigenvalues λ 1 + λ 2 + λ 3 = ∇ 2 ρ( r c ).…”
Bond critical point, local kinetic energy density, G(rc), and local potential energy density, V(rc), properties of the electron density distributions, rho(r), calculated for silicates such as quartz and gas-phase molecules such as disiloxane are similar, indicating that the forces that govern the Si-O bonded interactions in silica are short-ranged and molecular-like. Using the G(rc)/rho(rc) ratio as a measure of bond character, the ratio increases as the Si-O bond length, the local electronic energy density, H(rc)= G(rc) + V(rc), and the coordination number of the Si atom decrease and as the accumulation of the electron density at the bond critical point, rho(rc), and the Laplacian, inverted Delta2 rho(rc), increase. The G(rc)/rho(rc) and H(rc)/rho(rc) ratios categorize the bonded interaction as observed for other second row atom M-O bonds into discrete categories with the covalent character of each of the M-O bonds increasing with the H(rc)/rho(rc) ratio. The character of the bond is examined in terms of the large net atomic charges conferred on the Si atoms comprising disiloxane, stishovite, quartz, and forsterite and the domains of localized electron density along the Si-O bond vectors and on the reflex side of the Si-O-Si angle together with the close similarity of the Si-O bonded interactions observed for a variety of hydroxyacid silicate molecules and a large number of silicate crystals. The bond critical point and local energy density properties of the electron density distribution indicate that the bond is an intermediate interaction between Al-O and P-O bonded interactions rather than being a closed-shell or a shared interaction.
“…In short, the close similarity of the Si−O bond lengths and Si−O−Si angles and the electron density distributions for a quartz crystal and a gas-phase molecule like H 3 SiOSiH 3 implies that the forces that govern the two structures are short ranged and molecular-like. Also, the bond lengths and angles observed for a relatively large number of silica polymorphs such as quartz have been shown to conform closely with a potential energy surface calculated for the (OH) 3 SiOSi(OH) 3 molecule, again suggesting that the forces that govern the energy of the Si−O bond, Si−O bond lengths, and Si−O−Si angles are molecular-like. 1 Scatter diagrams of the bond critical point (bcp) properties plotted against the experimental bond lengths, R(Si−O) (squares), for a relatively larger number of silicate crystals: 23 (a) R(Si−O) vs ρ( r c ), the value of the electron density, ρ, at the bond critical point, r c ; (b) R(Si−O) vs r b (O), the bonded radius of the O atom; (c) R(Si−O) vs |λ 12 |, where λ 12 = 1/2(λ 1 + λ 2 ) and λ 1 + λ 2 measure the negative curvatures of ρ perpendicular to the bond path at r c ; (d) R(Si−O) vs λ 3 , the positive curvature of ρ measured parallel to the bond path at r c ; and (e) R(Si−O) vs ∇ 2 ρ( r c ), the Laplacian of ρ measured at r c .…”
Section: Si−o Bonded Interactions Of Hydroxyacid Silicate
Molecules A...supporting
confidence: 59%
“…Indeed, Gillespie and Johnson 16 have concluded that the bond comprising the H 3 Si−O−SiH 3 molecule is a highly ionic bond with net atomic charges conferred on Si and O of +3.02 and −1.72 e, respectively. Given the small bending force constant of the Si−O−Si angle, ∼5 N/m, calculated for the (OH) 3 Si−O−Si(OH) 3 molecule, together with a large net atomic charge on Si, it is difficult to reconcile why the angle observed for the molecule is bent at 144°, as observed for cristobalite, rather than straight if the bond is a closed-shell interaction and the charges on the Si atoms are large. Further, it is also notable that Cohen, in a first principles study of crystalline silica, concluded that “SiO 2 is held together by a combination of covalent spσ bonding and ionic bonding between the highly charged tetravalent Si 4+ and O 2- ions”.…”
Section: Si−o Bonded Interactions Of Hydroxyacid Silicate
Molecules A...mentioning
confidence: 99%
“…The electron density along the path at r c is at a minimum value with respect to any displacement parallel to the path but a maximum with respect to any radial displacement perpendicular to the path. The value of ρ( r c ) has been observed to be a direct measure of the strength of a given metal oxygen M−O bond; the greater the value of ρ( r c ), typically the shorter the bond . The trace of the Hessian of ρ( r ), H ij = ∂ 2 ρ( r )/∂x i ∂x j , when evaluated at r c and diagonalized equals the sum of eigenvalues λ 1 + λ 2 + λ 3 = ∇ 2 ρ( r c ).…”
Bond critical point, local kinetic energy density, G(rc), and local potential energy density, V(rc), properties of the electron density distributions, rho(r), calculated for silicates such as quartz and gas-phase molecules such as disiloxane are similar, indicating that the forces that govern the Si-O bonded interactions in silica are short-ranged and molecular-like. Using the G(rc)/rho(rc) ratio as a measure of bond character, the ratio increases as the Si-O bond length, the local electronic energy density, H(rc)= G(rc) + V(rc), and the coordination number of the Si atom decrease and as the accumulation of the electron density at the bond critical point, rho(rc), and the Laplacian, inverted Delta2 rho(rc), increase. The G(rc)/rho(rc) and H(rc)/rho(rc) ratios categorize the bonded interaction as observed for other second row atom M-O bonds into discrete categories with the covalent character of each of the M-O bonds increasing with the H(rc)/rho(rc) ratio. The character of the bond is examined in terms of the large net atomic charges conferred on the Si atoms comprising disiloxane, stishovite, quartz, and forsterite and the domains of localized electron density along the Si-O bond vectors and on the reflex side of the Si-O-Si angle together with the close similarity of the Si-O bonded interactions observed for a variety of hydroxyacid silicate molecules and a large number of silicate crystals. The bond critical point and local energy density properties of the electron density distribution indicate that the bond is an intermediate interaction between Al-O and P-O bonded interactions rather than being a closed-shell or a shared interaction.
“…The local kinetic energy density, G ( r c ), evaluated for the earth materials and molecules, is plotted against R(M−O) Å in Figure a. As observed for both ρ( r c ) and ∇ 2 ρ( r c ), G ( r c ) increases nonlinearly along two separate power law like trends with decreasing bond length, the lower trend in the figure consists of bonded interactions that involve first-row M atoms bonded to O and the upper consists of interactions that involve second-row M atoms bonded to O . The increase in G ( r c ) with decreasing bond length is expected, given that the values of ρ( r c ) and ∇ 2 ρ( r c ) both increase and that ∇ 2 ρ( r c ) is largely positive, particularly for the second-row M atoms.…”
Section: Introductionmentioning
confidence: 89%
“…An earlier calculation of the bond critical point properties for many earth materials shows that as the magnitudes of ∇ 2 ρ( r c ), ρ( r c ), and the three curvatures of ρ( r c ), λ i , each increase and the bonded radii of the M and O atoms and Δχ decrease, the M−O bond lengths decrease. As these results have been reported and examined elsewhere, , they will not be examined further here.…”
For a variety of molecules and earth materials, the theoretical local kinetic energy density, G(r(c)), increases and the local potential energy density, V(r(c)), decreases as the M-O bond lengths (M = first- and second-row metal atoms bonded to O) decrease and the electron density, rho(r(c)), accumulates at the bond critical points, r(c). Despite the claim that the local kinetic energy density per electronic charge, G(r(c))/rho(r(c)), classifies bonded interactions as shared interactions when less than unity and closed-shell when greater, the ratio was found to increase from 0.5 to 2.5 au as the local electronic energy density, H(r(c)) = G(r(c)) + V(r(c)), decreases and becomes progressively more negative. The ratio appears to be a measure of the character of a given M-O bonded interaction, the greater the ratio, the larger the value of rho(r(c)), the smaller the coordination number of the M atom and the more shared the bonded interaction. H(r(c))/rho(r(c)) versus G(r(c))/rho(r(c)) scatter diagrams categorize the M-O bonded interactions into domains with the local electronic energy density per electron charge, H(r(c))/rho(r(c)), tending to decrease as the electronegativity differences for the bonded pairs of atoms decrease. The values of G(r(c)) and V(r(c)), estimated with a gradient-corrected electron gas theory expression and the local virial theorem, are in good agreement with theoretical values, particularly for the bonded interactions involving second-row M atoms. The agreement is poorer for shared C-O and N-O bonded interactions.
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